A common training-only receiver-error assessment

The native contraction experiment preserves correctness but remains too broad for useful predictions. In parallel with that limitation, qualify a common error assessment using receiver observations alone. It must not let a poorly fitting Earth candidate inflate its own noise allowance.

Mathematical component

Use a fixed time-polynomial reference with degrees 3, 5 and 7. Any numerical reference coefficients may be used: their exact residual norm is at least the minimum over that fixed reference space. Use the conservative noise dimension n - p, counting every reference column, rather than an estimated SVD rank. No Earth-model residual, gyro value or future receiver position enters the source.

Qualify an exact-rational alternative to the existing lll.ilvis0_reference_scale.fixed_reference_scale. Define the discrete covariance law explicitly with one OU component, a constant offset, a linear drift and positive white noise. Record its rationalized fixed transition coefficients and all variances. Evaluate the residual quadratic form with scalar state-space innovations in rational arithmetic; do not build a whole-record dense covariance.

For a central chi-square with d degrees, inverse moments give

Choose a lower quantile floor using integer/rational comparisons, independently of observations. Noncentral lower-tail dominance and rank <= p then permit a conservative scale upper bound from any reference residual. Return an outward square-root endpoint checked against the exact rational quadratic form. An unsupported domain, precision limit or time allowance must abstain.

Test exact quadratic forms against independent small dense references, rank loss, poor reference means, quantile certificates, extreme numerical scales and cooperative precision/runtime limits. Benchmark generated prefixes before choosing an observed-source allowance. Preserve all earlier source freezes.

Recorded-data development assessment

Only after software qualification, freeze the first 292 receiver epochs of the already studied recording 570b37d23af5e245dd461051. Its later GPS positions are absent from the assessment API. Use an observation-independent coordinate chart with fixed latitude/longitude scales and height in metres; identify that chart separately from the older receiver-position-dependent error metric.

Predeclare two discrete correlation families corresponding approximately to 10-second and 300-second OU times. Their reference standard deviations are 0.3/0.3/0.7 chart metres for white error, and 1/1/3 for each correlated, offset and drift component. Anchor drift to training timestamps. Report all six covariance/reference combinations; do not choose one using model rankings.

Inputs, sources, chart, reference designs, covariance coefficients and finite work limits must freeze before calculation. Read saved receiver data only; zero original-IMU reads, native predictions, Earth-model fits or protected ESA evaluations. The assessment remains retrospective development.

Limits of the result

The method supplies a conservative scale under a declared Gaussian covariance law. It cannot establish that the law describes actual receiver errors or turn a reference residual into measured receiver accuracy. Mean misspecification can widen the bound. No automatic transfer to old covariance policies, other recordings, ESA, or production decisions is allowed.

This does not repair the wide nonlinear prediction ranges. Joint calibration structure, global numerical treatment, absolute withheld adequacy and independent confirmation remain separate requirements. No observed prediction fit follows from this component alone.

Saved prediction evidence · Native limitation · Earlier shared-scale mathematics · Roadmap.